Closed-Form Transmitter-Side Extraction of Receiver Resonance and Coupling Coefficient in Series–Series Compensated Wireless Power Transfer

Series–series (S–S) compensated wireless power-transfer (WPT) systems are increasingly deployed where connector-free and reliable energy delivery is required, but practical monitoring becomes ambiguous when receiver-resonance drift and magnetic-coupling variation produce similar transmitter-side impedance changes. This paper addresses that ambiguity by separating the two effects without receiver-side sensing. During a low-power diagnostic interval, the receiver terminal is briefly placed in open and short states, and only the fundamental phasors of the inverter output voltage and primary current are processed together with the known compensation capacitances. After the open-state measurement identifies the primary self-impedance, the short-state residual is mapped to an affine D–ω2 line; its zero crossing gives the receiver resonant frequency and secondary self-inductance, while its slope gives the mutual inductance and coupling coefficient. The routine is implementable as a start-up or periodic diagnostic function in WPT hardware that already measures the primary voltage and current and can impose the required receiver terminal states; it requires no receiver-side measurement, auxiliary sensing coil, short-loop resistance measurement, or iterative zero-phase search. In simulation, the coupling-coefficient error remained below 0.014% under receiver-inductance tolerance and mutual-inductance variation. In a prototype, the short-state data followed the predicted linear relation with R2=0.9979, and the extracted coupling coefficient agreed with the reference within about 5%. The identified receiver resonance was also used to guide operating-frequency adjustment in a practical power-transfer test.